marginalsatser

Marginalsatser is a term used in some Norwegian-language mathematical texts to describe a class of theorems about marginal quantities—quantities that arise when a larger object is reduced by aggregating, projecting, or considering only a subset of its components. The exact scope and terminology vary between fields, but the guiding idea is to relate margins to the original structure from which they are derived.

In probability and statistics, marginals are obtained from a joint distribution by summing or integrating over unwanted variables. Marginalsatser in this area address how marginal distributions relate to the joint distribution, and how properties such as normalization, independence, and conditional relationships are preserved or implied by marginalization. A typical expression is pX(x) = sum_y pXY(x,y) (discrete) or pX(x) = ∫ pXY(x,y) dy (continuous).

In combinatorics and matrix theory, margins refer to row and column sums of a matrix or contingency table. Marginalsatser here may concern the existence of matrices with given margins, inequalities that constrain possible margins, or the relationship between margins and the overall structure (for example, the Gale–Ryser theorem for 0-1 matrices with prescribed margins).

Across fields, marginalsatser serve to formalize how marginal information reflects or constrains the larger object. They are useful in proofs that switch between global structures and their marginals, and in methods that rely on aggregating data or projecting high-dimensional objects to lower dimensions.

See also: marginal distribution, marginalization, contingency tables, Gale–Ryser theorem.